Using sine wave excitation and frequency domain measurements, such as bioimpedance measurements is common approach in assessing passive electrical properties of different objects, such as biological object. However, frequency sweeping or hopping of a sine wave excitation over a wide frequency range is too slow for performing impedance spectroscopy to recover fast impedance changes in biological objects such as caused by single cells and cell cultures in high throughput microfluidic devices (lab-on-a-chip type analyzers and micro-reactors). The use of short-time and broad frequency band single-pulse excitation and monitoring the response as a function of time is informative and will greatly reduce the measurement interval (Pliquett et al., 2000).
Chirp signals, i.e. multi-cycle sine wave based signals in which the frequency increases (‘up-chirp’) or decreases (‘down-chirp’) continuously as a function of time, are widely used in radar and sonar applications, acoustic, ultrasonic, optical and seismological studies (Pollakowski and Ermert, 1995; Müller and Massarani, 2001; Misairidis and Jensen, 2005; Rufer et al., 2005). The main advantage of chirp signals is their well defined frequency range (from start to stop frequency of the chirp) and constant or accurately predetermined power spectral density, PSD, for wide range of frequencies, also acceptable crest factor and signal-to-noise ratio (Müller and Massarini, 2001; Misairidis and Jensen, 2005). Recently, using of chirp and modified (e.g. windowed) chirp signals is proposed for estimation of the frequency response of electrical impedance (the impedance spectrum), particularly of biological objects (Min et al., 2007a; Paavle et al., 2008 and 2009; Nahvi and Hoyle, 2008 and 2009; Hoyle and Nahvi, 2008). Suitable signal processing methods are introduced by Vaseghi, 2006 and Chu, 2008.
Using of rectangular chirps is also known (Pollakowski and Ermert, 1994; Rufeert et al., 2005). Signal processing is much simpler for rectangular wave excitation with only constant binary values, +A, and −A. Moreover, the rectangular waveforms have the minimally possible unity value crest factor (ratio of a peak value to a root-mean-square level). A widely used method is to generate a pseudo-random maximum length sequence (MLS) of rectangular signals (Sun et al., 2007a 2007b 2009; Gawad et al., 2007). Also, rectangular chirp signal which can be described as a signum-chirp function instead of the classical sinusoidal chirp is proposed. Besides the simplest rectangular chirp having non-return-to-zero (NRZ) pulses (binary chirp, zero-states are absent), some versions of return-to-zero (RZ) rectangular pulse chirp function (ternary chirp, +A; 0; −A values) have been suggested for excitation waveforms (Min et al., 2007b, 2009b, 2009c; Paavle et al., 2009, 2010). Using of chirp signals (both, based on sine wave and rectangular wave) have several advantages, including short excitation and measurement time and well determined excitation bandwidth (frequency range), so that the most of generated energy (85 to 99%) is concentrated into the useful bandwidth, and constant level or otherwise specified power spectral density (PSD) within the useful bandwidth (Min et al, 2009a). This is true, if the number of cycles in chirp is minimally about 100, and will be exact, if the number of cycles is 100,000 and higher. At a low number of cycles the spectrum becomes significantly distorted. The distortions become very large, if the number of cycles goes lower than 10.
However, the spectroscopy of dynamic objects with rapidly changing impedances is still challenging as it is commonly assumed that chirps contain hundreds, thousands, and even millions of signal cycles at high frequencies. Very fast changing impedances, as in the case of moving objects as bacteria, cells, droplets, bubbles, etc. in microfluidic devices, require a very short excitation time to avoid the dynamic errors of spectrogram (primarily of the timeline sequence of spectral snapshots) due to the quick changes. Another similar example is the pulsating impedance of the cardiovascular system of living organisms.
What is needed, therefore, is a fast measurement method scalable in both time and frequency domain for flexible performing of impedance spectroscopy of dynamic impedances.
What is also needed is that as much as possible energy of the signal is generated within the excitation bandwidth to minimize the power consumption, getting better signal-to-noise ratio, and avoiding the heating or other unwanted effects on the object due to out-of-bandwidth components of the excitation signal.